# Spatial Strategies, Not Actions: Vector-Quantized Geodesics as Tools for LLM-Driven Agents

arXiv: https://arxiv.org/abs/2610.00613 · HTML: https://mlsanity.com/paper/2610.00613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal and embodied agents, one of 16 directions in LLM agents and tool use.
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

## Builds on (most cited first, 12 of 12)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [CityEQA: A Hierarchical LLM Agent on Embodied Question Answering Benchmark in City Space](https://mlsanity.com/paper/2502.12532/) (2025)
- [Guide-LLM: An Embodied LLM Agent and Text-Based Topological Map for Robotic Guidance of People with Visual Impairments](https://mlsanity.com/paper/2410.20666/) (2024)
- [Huber-energy measure quantization](https://mlsanity.com/paper/2212.08162/) (2022)
- [CubeBench: Diagnosing Interactive, Long-Horizon Spatial Reasoning Under Partial Observations](https://mlsanity.com/paper/2512.23328/) (2025)
- [Diversity in deep generative models and generative AI](https://mlsanity.com/paper/2202.09573/) (2022)
- [Vision-Based Localization and LLM-based Navigation for Indoor Environments](https://mlsanity.com/paper/2508.08120/) (2025)
- [From Pixels to BFS: High Maze Accuracy Does Not Imply Visual Planning](https://mlsanity.com/paper/2603.26839/) (2026)
- [LLMs for Text-Based Exploration and Navigation Under Partial Observability](https://mlsanity.com/paper/2604.09604/) (2026)

## Abstract (arXiv)

Large language model (LLM) based agents are often criticized for lacking spatial understanding and mainly exploiting statistical text patterns. We investigate their spatial comprehension through an architecture combining geometrical tools with a LLM serving as a high-level orchestrator in grid-world environments. The agent first collects geodesic trajectories, which are then vector-quantized to extract a representative subset. Offline, the LLM associates a natural language description of the underlying behavioral patterns to each selected trajectory, making it a tool. Online, the LLM chooses the appropriate tool conditioned on the current state and goal. Low-level control is handled by primitive actions that execute the trajectory associated with the tool. From an agentic AI perspective, this approach separates learning into two levels: tool discovery is handled through unsupervised quantization of trajectories, while reasoning and decision-making are handled by the LLM. We test the approach in a partially observable dynamic 2D grid environment with an open vision-language model (Qwen3.6-35B-A3B). Pairing the geometry-derived tool library with an agent-centered zoom tool and a collision detection tool lets a fast, non-reasoning configuration match the goal-reaching rate of a much more costly chain-of-thought version, while cutting the cost of a decision from minutes to seconds.